When air blows between them somehow (by air can, by blowing with your mouth, by swiping a hand between them, etc.), the Venturi effect occurs. The Venturi effect is also demonstrated by the Venturi meter and states that faster air/fluid reduces pressure. Thus, when the air between the balloons moves faster than the air outside them, the outside pressure causes them to come together.

For this demo, two balloons are set hanging next to each other.

When air blows between them somehow (by air can, by blowing with your mouth, by swiping a hand between them, etc.), the Venturi effect occurs. The Venturi effect is also demonstrated by the Venturi meter and states that faster air/fluid reduces pressure. Thus, when the air between the balloons moves faster than the air outside them, the outside pressure causes them to come together.